Article ID: | iaor20084527 |
Country: | United States |
Volume: | 2006 |
Issue: | 18109 |
Start Page Number: | 1 |
End Page Number: | 22 |
Publication Date: | Jan 2006 |
Journal: | Journal of Applied Mathematics and Stochastic Analysis |
Authors: | Zhang Q., Yin G., Liu R.H. |
Keywords: | markov processes, stochastic processes |
This paper is concerned with fast Fourier transform (FFT) approach to option valuation, where the underlying asset price is governed by a regime-switching geometric Brownian motion. An FFT method for the regime-switching model is developed first. Aiming at reducing computational complexity, a near-optimal FFT scheme is proposed when the modulating Markov chain has a large state space. To test the FFT method, a novel semi-Monte Carlo simulation algorithm is developed. This method takes advantage of the observation that the option value for a given sample path of the underlying Markov chain can be calculated using the Black–Scholes formula. Finally, numerical results are reported.